Calculus Examples

$2 x^{\frac{1}{3}}$

Step 1

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int x^{\frac{1}{3}} d x$

Step 2

By the Power Rule, the integral of $x^{\frac{1}{3}}$ with respect to $x$ is $\frac{3}{4} x^{\frac{4}{3}}$ .

$2 (\frac{3}{4} x^{\frac{4}{3}} + C)$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Rewrite $2 (\frac{3}{4} x^{\frac{4}{3}} + C)$ as $2 (\frac{3}{4}) x^{\frac{4}{3}} + C$ .

$2 (\frac{3}{4}) x^{\frac{4}{3}} + C$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

Combine $2$ and $\frac{3}{4}$ .

$\frac{2 \cdot 3}{4} x^{\frac{4}{3}} + C$

Step 3.2.2

Multiply $2$ by $3$ .

$\frac{6}{4} x^{\frac{4}{3}} + C$

Step 3.2.3

Cancel the common factor of $6$ and $4$ .

Tap for more steps...

Step 3.2.3.1

Factor $2$ out of $6$ .

$\frac{2 (3)}{4} x^{\frac{4}{3}} + C$

Step 3.2.3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.3.2.1

Factor $2$ out of $4$ .

$\frac{2 \cdot 3}{2 \cdot 2} x^{\frac{4}{3}} + C$

Step 3.2.3.2.2

Cancel the common factor.

$\frac{2 \cdot 3}{2 \cdot 2} x^{\frac{4}{3}} + C$

Step 3.2.3.2.3

Rewrite the expression.

$\frac{3}{2} x^{\frac{4}{3}} + C$